Finite Group Databasebeta

← Group #72319364

Character table — Group #72319364

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size112222244444444444444444444444888888888888888888888888816161616161616161616161616161616161616161616161616161616163232323232323232323232323232323232323232323232326464646464646464
order122448822244444448888816161616161616162244444444888888816161616161616168881616161616161616161632323232323232323232323232323232222222444444444432323232323232321616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111-1-11111111111111-1-1-1-1111-1-1-1111-1-11111111111-1-1-1-1-1-1-111-1-1-1-11111111111111111111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111-1-11111111111111-1-1-1-1111-1-1-1111-1-11111111111-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1111-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111-1-11111111111111-1-1-1-1111-1-1-1111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-11111-1-1-1-111111111-1-1-1-11111
χ8111111111111111-1-11111111111111-1-1-1-1111-1-1-1111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111111111111111-1-1-1-1
χ91111111111111-1-11111-1-11-1-1-1-1-1-1-1-11-11-1-1-1-11-1-111-111-1-1-1-1-1-111111-1-111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-111-1-1-111-1-111-1-1iiii−i−i−i−iii−i−iii−i−i
χ101111111111111-1-11111-1-11-1-1-1-1-1-1-1-11-11-1-1-1-11-1-111-111-1-1-1-1-1-111111-1-111-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11-1-1111-1-111-1-111iiii−i−i−i−i−i−iii−i−iii
χ111111111111111-1-11111-1-11-1-1-1-1-1-1-1-11-11-1-1-1-11-1-111-111-1-1-1-1-1-111111-1-111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-111-1-1-111-1-111-1-1−i−i−i−iiiii−i−iii−i−iii
χ121111111111111-1-11111-1-11-1-1-1-1-1-1-1-11-11-1-1-1-11-1-111-111-1-1-1-1-1-111111-1-111-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11-1-1111-1-111-1-111−i−i−i−iiiiiii−i−iii−i−i
χ131111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i11-1-1-11-1111-1-1-1-111−i−i−i−iiiiiii−i−i−i−iii
χ141111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1111-11-1-1-11111-1-1−i−i−i−iiiii−i−iiiii−i−i
χ151111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii11-1-1-11-1111-1-1-1-111iiii−i−i−i−i−i−iiiii−i−i
χ161111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1111-11-1-1-11111-1-1iiii−i−i−i−iii−i−i−i−iii
χ1711111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-11-1-11-11-11-11-1ii−i−iii−i−ii−ii−ii−ii−i
χ1811111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-11-111-11-11-11-11ii−i−iii−i−i−ii−ii−ii−ii
χ1911111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-11-1-11-11-11-11-1−i−iii−i−iii−ii−ii−ii−ii
χ2011111111-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1111-1-11111-1-1-1-1-11-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-11-111-11-11-11-11−i−iii−i−iiii−ii−ii−ii−i
χ2111111111-1-11-1-111-1-111111-1-1-1-1-1-1-1-11-11-11-1-1-111-1-11-1-1-1-11111-1-1-1-11-1111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-11-1-111-11-1-11-11−i−iii−i−iiii−ii−i−ii−ii
χ2211111111-1-11-1-111-1-111111-1-1-1-1-1-1-1-11-11-11-1-1-111-1-11-1-1-1-11111-1-1-1-11-1111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-11-11-111-1-11-111-11-1−i−iii−i−iii−ii−iii−ii−i
χ2311111111-1-11-1-111-1-111111-1-1-1-1-1-1-1-11-11-11-1-1-111-1-11-1-1-1-11111-1-1-1-11-1111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-11-1-111-11-1-11-11ii−i−iii−i−i−ii−iii−ii−i
χ2411111111-1-11-1-111-1-111111-1-1-1-1-1-1-1-11-11-11-1-1-111-1-11-1-1-1-11111-1-1-1-11-1111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-11-111-1-11-111-11-1ii−i−iii−i−ii−ii−i−ii−ii
χ2511111111-1-11-1-1-1-11111-1-1111111111-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-11-1-1111-1-111-1-1111-1-1-1-1111-1-111-1-11
χ2611111111-1-11-1-1-1-11111-1-1111111111-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-111-1-1-111-1-111-111-1-1-1-111-111-1-111-1
χ2711111111-1-11-1-1-1-11111-1-1111111111-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1-11-1-1111-1-111-1-11-1-11111-1-1-111-1-111-1
χ2811111111-1-11-1-1-1-11111-1-1111111111-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-111-111-1-1-111-1-111-1-1-11111-1-11-1-111-1-11
χ2911111111-1-11-1-1-1-1-1-111-1-11111111111111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1111-11-1-11-111-1-1-11111-1-11-1-11-111-1
χ3011111111-1-11-1-1-1-1-1-111-1-11111111111111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-11-111-11-1-11-1-11111-1-1-111-11-1-11
χ3111111111-1-11-1-1-1-1-1-111-1-11111111111111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111-11-1-11-111-111-1-1-1-111-111-11-1-11
χ3211111111-1-11-1-1-1-1-1-111-1-11111111111111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-11-111-11-1-1111-1-1-1-1111-1-11-111-1
χ332222222222222222222222-2-2-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222-2-222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2222-2-222-2-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000000000000000
χ352222222222222-2-22222-2-22222222222-22-2-2-2-22-2-222-222-2-22222-2-2-2-22-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ362222222222222-2-2-2-222-2-2222222222-22-22-2-2-2-22222-2-2-2-2-22222-2-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-22-2-222222222222222222-22-222-2-22-2-2-2-2222-2-2-2-2-2-22222-22-222-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-22-2-222-2-222222222222222-22-22-2-2-222-2-22-2-2-2-2-2-2-2-222222-22-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-22-2-2-2-22222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2222222222222-2-222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-22-2-2-2-2-2-222-2-22-2-2-2-2-2-2-2-22222-222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ412222222-22-2-22-22200-2-22222222-2-2-2-20000-22-20002-2-2002-222-2-222-2-200000002-20000000000000000000000022-20-20000-2-2220000000000000000
χ422222222-22-2-22-22200-2-22222222-2-2-2-20000-22-20002-2-2002-222-2-222-2-200000002-200000000000000000000000-2-2202000022-2-20000000000000000
χ432222222-22-2-22-22200-2-2222-2-2-2-222220000-22-20002-2-2002-2-2-222-2-2220000000-22000000000000000000002-2-200020-222-200000000000000000000
χ442222222-22-2-22-22200-2-2222-2-2-2-222220000-22-20002-2-2002-2-2-222-2-2220000000-2200000000000000000000-222000-202-2-2200000000000000000000
χ452222222-22-2-22-2-2-200-2-2-2-222222-2-2-2-200002-220002-2200-2222-2-2-2-2220000000-22000000000000000000002-22000-20-22-2200000000000000000000
χ462222222-22-2-22-2-2-200-2-2-2-222222-2-2-2-200002-220002-2200-2222-2-2-2-2220000000-2200000000000000000000-22-2000202-22-200000000000000000000
χ472222222-22-2-22-2-2-200-2-2-2-22-2-2-2-2222200002-220002-2200-22-2-22222-2-200000002-200000000000000000000000222020000-2-2-2-20000000000000000
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χ502222222-2-22-2-222200-2-22222222-2-2-2-20000-2-22000-22-200-22-2-22222-2-20000000-2200000000000000000000-2-220002022-2-200000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.